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Centre for Employment Studies
A
finitary characterization of Ewens sampling formula
(download)
D. Costantini *
U. Garibaldi **
P.Viarengo ***
Abstract
The clustering of agents in the market is a typical problem dealt with
by the new approaches to macroeconomic modeling, that describe
macroscopic variables in terms of the behavior of a large collection of
microeconomic entities. Clustering has a lot of economical
interpretations, that are often described by Ewens Sampling Formula
(ESF). This formula can be traced back to Fisher as “species sampling”,
and its main use was restricted to Genetics for a long time. Contrary
to the usual complex derivations [17], we suggest a finitary
characterization of the ESF pointing to real economic processes. Our
approach is finitary in the sense that we probabilize a system of n
individuals considered as
a closed system, a population, where individuals can change attributes
as time moves on. The intuitive meaning of the probability is the
fraction of time the system spends in the considered state of
clustering. As ESF is an equilibrium distribution satisfying the
detailed balance, some cumbersome properties are derived in a simple
way.
* Clinical
Epidemiology, National Cancer Research Institute, Genoa, Italy
** IMEM-CNR, c/o Department of Physics, University of Genoa, Italy
*** National Cancer Research Institute (IST), Genoa, Italy and
Department of Statistical Science, University of Bologna, Bologna, Italy
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